How do they draw contour lines?

[Colophon]

I’ve often wondered how cartographers plot contour lines on topographical maps. Google has been able to tell me its done from aerial photography using a technique called stereo photogrammetry, either by a person looking through a stereo viewer at two aerial photos taken from different angles, or these days more likely on a computer screen, but details are lacking.

So, anyone know exactly how they figure out where to draw all those little brown lines?

[Ice_Wolf]

I would have thought the lines join together common points that share the same height from sea level, with flatter land having lines further apart, and hilly country showing the lines tighter together.

Wouldn’t part of it be down to a measurement of how far above sea level?

[plnnr]

Plot elevations. Connect the dots. Voila’. Or at least that’s how we did it in air photo interpretation class.

[Colophon]

Yes, I know what the lines represent, but I’d like to know how you actually obtain the height data by squinting at the photos. It must be fairly straightforward, as contours are plotted seemingly very intricately and accurately (at least on British Ordnance Survey maps - look at this area, for instance. If you were just joining up various spot heights, you’d never get that level of accuracy. Is there some “continuous” way of tracing along a line of equal height that they use?

[RM_Mentock]

A lot of the surface of the Earth has been surveyed many times, by civil and geological survey, to get altitude data. There are mathematical algorithms to take aerial photometry and produce similar altitude data. Regardless, you end up with a finite number of data.

But there are other mathematical algorithms for taking such data points and producing the continuous contour lines that you see on the maps. For a simple example, if you had two data points 10 meters apart, and one point had an altitude of 103 meters and the other had an altitude of 93 meters, then the 100 meter contour would pass through a point 3 meters from the first point. Of course, that assumes that the land is a straight line from point to point, but it might be close enough for purposes of the map.

The algorithm for a two dimenional set of data (they don’t even have to be evenly spaced) is more complicated, and there are a lot of even more complicated algorithms that take other factors into account.

[Yossarian]

Using sterophotos, if you know the parallax and height of the airplane taking the photos, you can quantitatively calculate the relief (relative elevation differences) of the area in the photographs. (See http://mercator.upc.es/tutorial/nicktutor_11-4.html)

Combine this with ground survey data, which provides the absolute values for elevation for specific points (benchmarks), and you’ve got yourself elevation contour lines.

Of course, that’s the old way. I think modern elevation and bathymetry measurements are done with LIDAR satellites.

[jjimm]

Talking about the days before aerial photography though - how many benchmark points would have to have been taken for a map like the British Ordnance Survey one linked earlier? That sounds like a lot of work.

[Yossarian]

From http://mac.usgs.gov/isb/pubs/booklets/topo/topo.html

Initially charged by Congress with the “classification of the public lands,” the USGS began topographic and geologic mapping in 1879. Most of the early USGS mapping activities took place in the vast, largely uninhabited Western United States.

Extreme challenges awaited these mapping pioneers. Travel was arduous and costly. Many locations could be reached only by mule pack train. Furthermore, surveying and mapping instruments were crude by today’s standards. Most maps were made using a classic mapping technique called planetable surveying.

Planetable surveying took great skill and, depending on the mapping site, equal daring. Carrying a planetable–essentially a portable drawing board on a tripod with a sighting device–the topographer would climb to the area’s best vantage point and carefully plot on the map those features that could be seen and measured in the field. Planetable surveying remained the dominant USGS mapping technique until the 1940’s, when it gave way to the airplane and the age of photogrammetry.

[ticker]

The benchmark points - known as Trig Points in OS speak - are actually not that close together. You can see one on the small map r_k linked to. It is the light blue triangle at the top of Fell of Barhullion. Before aerial photography contour maps were rare and very much less detailed. For an example go to and do a Co-ordinate search on ‘296900,219400’ (can be very slow at times). Compare that result from 1890 with the up-to-date map [url=“http://www.streetmap.co.uk/newmap.srf?x=296900&y=219400&z=3&sv=296900,219400&st=4&mapp=newmap.srf&searchp=newsearch.srf”]here

[Colophon]

Thanks for that link, Pantellerite. This is what I was looking for:

Use of the above devices to specify a large enough number of elevation points in stereo photos to permit contouring is difficult and tedious. Sophisticated optical-mechanical stereoplotters are applied instead. These use two or three movable projectors that pass light through stereo pairs made into glass-mounted film diapositives onto a tracing table (platen) which can be raised and lowered. A 3-D image or stereomodel is produced which can be viewed by an outside observer by some filter method (for black and white photos, this is done by the anaglyph method in which one photo is projected through a red filter and the other a cyan filter and then viewed through eyeglasses with corresponding color filters). A small point of light or dot is projected onto the stereomodel. When the dot appears to coincide with some part of the model surface (as seen through the viewer), that dot locates a particular elevation determined by the platen height and calibrated by control points. An experienced operator can then move the light along the model surface such that it always remains coincident. This motion traces a contour line. The platen table is then raised (or lower) a fixed amount determined by the contour interval chosen and the next elevation is contoured, and so on until the entire surface is thus traced. Today, analytical stereoplotters are capable of semi-automating the contouring through computer processing of mathematically transformed data.

[Yossarian]

Sophisticated optical-mechanical stereoplotters are applied instead. These use two or three movable projectors that pass light through stereo pairs made into glass-mounted film diapositives onto a tracing table (platen) which can be raised and lowered.

I just wanted to note that we’ve got one of these beasts in a downstairs lab. It’s as complicated as it is huge; I’ve not yet tried to use it–heck, I can’t even figure out where to begin!